Supplement 1. R code for the SES (standardized effect sizes) bootstrapping procedures and the hierarchy of linear mixed models of individual tree growth.

File List BootstrapSES.R: R code demonstrating how to compute diversity effects as standardized effect size (SES) following Potvin and Gotelli (2008) for both (i) plot-level overyielding and (ii) comparison among canopy statuses.<br> (md5: 0b9c6fc3752d601e7660515eb0505159) MultilevelModeling.R: R code for fitting and comparing the relative support for a hierarchy of linear-mixed models of individual tree growth. R code demonstrating how to compute confidence intervals with a bias-corrected bootstrap method.<br> (md5: c73e3dec4e1059c7c518fe1a07a416fa) Description BootstrapSES.R generates random data conforming to our experimental design (part 0) and tests for overyielding (part 1) using our modified version of the bootstrap methods developed by Potvin and Gotelli (2008). The bootstrap procedure is then used to compare the magnitude of overyielding among canopy statuses (part 2). Part 1 and part 2 could be directly applied to any data.frame containing columns similar to that of “data”, which is fully described at the end of part 0. MultilevelModeling.R requires the lme4 package to fit linear-mixed models. First, methods are defined to generate random tree growth data (simulateData()), to perform bootstrap likelihood ratio tests (bootLRT()), and to compute confidence intervals following a bias-corrected percentile method (see Efron and Tibishrani, 1986; BCconf()). The rest of the code generates random data, fits a hierarchy of linear-mixed model of tree growth, compares the models based on AIC and computes confidence intervals for the most complex example model.